The model’s distances isn't proportional to the actual dimensions of the solar system as B. No, because the ratios of model length to actual distance are different for the two planets.
What is ratio?Ratio demonstrates how many times one number can fit into another number. It is used to show the comparison between two or more things
In this case, in model, the distance from the sun to Earth is 7 inches and the distance from the sun to Neptune is 19 inches. This can be illustrated as:
= 7/19
= 0.368
If the actual distance from the sun to Earth is 91.549 million miles and the actual distance from the sun to Neptune is 2,780.5 million miles, the ratio is:
= 91.549 / 2780.5
= 0.0329
Therefore, since they're different numbers, the information doesn't illustrate a proportional ratio.
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100 points 2 questions
Question 1
There are 140 people in a theater watching a movie. The number of children present is 3 times the number of adults. How many children are watching the movie?
12 children
35 children
3 children
105 children
question 2
A catering company pays cooks $85 per shift and waiters $45 per shift. Yesterday, 10 people worked for the company at a special event. If the total amount paid to the employees was $570, how many cooks worked at the event?
3 cooks
7 cooks
10 cooks
12 cooks
Answer:
105 Children and 3 cooks
Step-by-step explanation:
I took the test :)
a) The total number of children watching the movie is 105 children
b) The total number of cooks that worked at the event is 3 cooks
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
a)
Let the number of children be = a
Let the number of adults be = b
Let the total number of people in the theater be = 140
Now , the equation will be
a + b = 140 equation (1)
And , the number of children present is 3 times the number of adults
So ,
a = 3b
Divide by 3 on both sides of the equation , we get
b = a/3
Substituting the value of b in equation (1) , we get
a + b = 140
a + a/3 = 140
( 4a ) / 3 = 140
Multiply by 3 on both sides of the equation , we get
4a = 420
Divide by 4 on both sides of the equation , we get
a = 105
Therefore , the value of a is 105 and the number of children watching the movie is 105 children
b)
Let the number of cooks be = x
Let the number of waiters be = y
Let the amount for each cook be = $ 85
Let the amount for each waiter be = $ 45
The total number of workers = 10
Now , the equation will be
x + y = 10 be equation (1)
The total amount paid to the employees be = $ 570
Now , the equation will be
85x + 45y = 570 be equation (2)
On simplifying equation (1) and equation (2) , we get
Multiply equation (1) by 45 , we get
45x + 45y = 450 be equation (3)
Subtract equation (3) from equation (2) , we get
40x = 120
Divide by 3 on both sides of the equation , we get
x = 3
Therefore , the value of x is 3 and the number of cooks that worked in the event is 3 cooks
Hence ,
a) The total number of children watching the movie is 105 children
b) The total number of cooks that worked at the event is 3 cooks
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Melanie recorded a tape of her guitar playing. It cost her $2,700 to record the master tape, and it costs $2.50 to make each copy. If she sells the tapes for $10 each, how many tapes must she sell to break even?
The number of tapes Melanie must sell to break even is 360 tapes.
How to find the number of tapes Melanie must sell to break even?To find the number of tapes Melanie must sell to break even, we must follow these steps.
We must identify how much she earns for each tape that she sells, for this we must subtract the sale price of each tape, by the value that she pays to make each tape.
10 - 2.5 = 7.5Now we must divide the total cost of the mother tape by the profit she makes on each tape she sells.
2,700 / 7.5 = 360Based on the above, we can infer that she must sell 360 tapes to cover the value of the mother tape and each of the tapes that she needs to sell. Next it is checked:
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Find the equation (in slope-intercept form) of the line passing through the points with the given coordinates.
(5,3) , (4,1)
The equation (in slope-intercept form) of the line passing through the points (5,3) and (4,1) is y = 2x -7
How to find equation of a line in slope intercept form?The equation of a line in slope intercept form can be represented as follows:
y = mx + c
where
m = slope of the linec = y-interceptlet's find the slope as follows:
(5, 3)(4, 1)
m = 1 - 3 / 4 - 5
m = - 2 / -1
m = 2
Therefore, let's find the y-intercept using (4, 1)
y = 2x + c
1 = 2(4) + c
c = 1 - 8
c = -7
Therefore, the equation of the line is y = 2x -7
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examples of direct variation with nonzero numbers
A direct variation with nonzero numbers is if y varies directly as x, and y = 6 when x = 2,
What is direct variation?The relationship between two variables in which the variables have a constant ratio, k, where k is not equal to 0.
K is known as the constant. Assume the variables are x and y, and that y varies directly with x. We can say that the y/x ratio is equal to k, where k is not equal to zero.
This formula can also be written as y = kx where k is not equal to 0.
It's critical to understand that we can use these two ratios interchangeably depending on the problem at hand.
In the example given, the constant of variation is k = = 3. Thus, the equation describing this direct variation is y = 3x.
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The temperature in Quebec City was 5°C at 4 pm. By midnight, the temperature dropped 15 degrees.
-20
A B
0 5
Point A
O Point B
Point C
Point D
Which point is a representation of the colder midnight temperature in degrees Celsius?
D
Mark this and return
Save and Exit
Next
Submit
4
A is the Point of representation of the colder midnight temperature in degrees Celsius.
The temperature in Quebec City was 5°C at 4 pm. By midnight, the temperature dropped 15 degrees.
To find out which point is a representation of the colder midnight temperature in degrees Celsius:
We know that the temperature dropped 15 degrees, and that it was initially of 5°C. So, by midnight, the temperature will be of -10°C (5-15=-10).
We also know that the distance between points is of 5°C. So, the point that we have to mark is point A, which represents -10°C.
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ANSWER PLEASE sorry forgot the caps
Answer:
option 1
Step-by-step explanation:
for every 10 students 4 like mathematics , then
80 ÷ 10 = 8
so 8 × 4 = 32
it is predicted that out of 80 students 32 like mathematics
3q-9\le
3q−9≤
\,\,8q+10
8q+10
The value of q after solving the inequality, 3q-9 ≤ 8q+10, is q ≤ -19/5.
According to the question,
We have the following information:
3q-9 ≤ 8q+10
Adding 9 to both sides of the inequality:
3q ≤8q+10+9
3q ≤ 8q+19
Subtracting 8q from both sides of the expression:
3q-8q ≤ 19
-5q ≤ 19
Dividing both sides by -5:
q ≤ -19/5
(More to know: inequalities can solved like an equation but the only difference is that the sign of equal has to be replaced by the signs of inequality.)
Hence, the value of q after solving the inequality, 3q-9 ≤ 8q+10, is q ≤ -19/5.
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Melanie Inc. has sales equal to $300,000 for the year. Its Accounts receivable balance is $100,000 and is made up of $50,000 30 days old, $20,000 60 days old, $11,000 90 days old and $19,000 over 120 days old. It has a debit balance of $400 in Allowance for Doubtful Accounts. The rate of uncollectibility is as follows: 1% in the 1-30 days category, 3% in the 31-60 days category, 5% in the 61 to 90 days category and 25% over 120 days.
What is the balance in Bad Debts Expense for the year?
• $6,200
$6,400
• $6,800
• $6,000
The balance on the Bad Debt Expense account for the year, based on the accounts receivable balance and the rates of uncollectibility is $6, 800.
How to find the balance on bad debt expense?First, find the uncollected receivables estimate for the year using the rates of uncollectibility.
= ∑ (Age of receivable x Rate of uncollectibility)
= (50, 000 x 1%) + ( 20,000 x 3%) + (11, 000 x 5%) + (19, 000 x 25%)
= 500 + 600 + 550 + 4, 750
= $6, 400
The Bad Debts Expense for the year would then be:
= Uncollected receivables estimate + Debit balance on Allowance for doubtful accounts
= 6, 400 + 400
= $6, 800
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UpEx delivers packages which cost $1.50 per package to deliver. The fixed cost to run the delivery truck is $198 per day. If the company charges $3.50 per package, how many packages must be delivered daily to make a profit of $32?
The number of packages that need to be delivered daily by UpEx to make a profit of $32 is 115 packages
How to find the number of packages?First, find the contribution margin of each package:
= Charge to deliver package - Cost to deliver package
= 3.50 - 1.50
= $2.00
To find the number of packages needed to make a profit of $32, the formula is:
= (Fixed cost + projected profit) / Contribution margin
= ( 198 + 32) / 2
= 230 / 2
= 115 packages
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A candy company wants to produce 30 kilograms of a special 30% fat content chocolate to conform with customer
dietary demands. To obtain this, a 50% fat content imported chocolate is combined with a 20% fat content domestic
chocolate in a special melting process. How many kilograms of the 50% fat content chocolate and how many kilograms
of the 20% fat content chocolate are used to make the required 30 kilograms?
amount of 50% fat content chocolate = 10 kg
amount of 20% fat content chocolate =
kg
***
10 kilograms of the 50% fat-content chocolate and 20 kilograms of the 20%, fat-content chocolate are used to make the required 30 kilograms.
What is an equation?Equations are statements that affirm the equivalence of two expressions that are joined by the equals symbol "=". An equal sign ("=") links two expressions together to form an equation.
The two expressions on each side of the equals sign are referred to as the "left-hand side" and "right-hand side" of the equation. The right side of an equation is typically assumed to be zero. Since we can balance this by deducting the expression on the right from the expressions on both sides, this won't reduce the generality.
Suppose the amount of 50% fat content chocolate is x and the amount of 20% fat content chocolate is y,
Since the candy company wants to produce 30 kilograms,
x+y=30 -----(1)
If a candy manufacturer wishes to meet the dietary requirements of its customers, it may make 30 kg of special chocolate with a 30% fat content. A specific melting procedure is used to blend local chocolate with 20% fat content with foreign chocolate with 50% fat content to create this. The resultant equation reads,
50x + 20y = 30(30)
5x+2y=90 -------(2)
After solving the equation 1 and 2 we get,
x=10
y=20
Thus, 10 kilograms of the 50% fat-content chocolate and 20 kilograms of the 20%, fat-content chocolate are used to make the required 30 kilograms.
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these are the first five terms in a Fibonacci sequence.
1 5 6 11 17
Write down the next two terms in the sequence.
Answer: 28 and 45
Step-by-step explanation: you add 11 and 17 to get 28 and then add 28 and 17 to get 45
hii! could someone help with this?
The projected cash receipts for April and the projected cash receipts for May can be found to be:
April - $187, 500May - $206, 250How to find the projected cash receipts?The projected cash receipts in April would be:
= ( 25% x Projected sales for April ) + ( 75% x Projected sales for March)
= (25% x 210, 000) + ( 75% x 180, 000)
= 52, 500 + 135, 000
= $187, 500
The projected cash receipts for May is then:
= ( 25% x Projected sales for May ) + ( 75% x Projected sales for April )
= ( 25% x 195, 000) + ( 75% x 210, 000)
= $ 48, 750 + 157, 500
= $206, 250
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Determine the domain and range of the graph of the transformed function shown
The domain is the set of all real numbers and the range is:
R: (-∞, 4]
How to determine the domain and range of the graph?
For any function, we define the domain as the set of possible inputs, the ones in the horizontal axis, and the range as the set of the output, the ones in the vertical axis.
We can see that we have a parabola that in the bottom part has two arrows, so it extends in the wole domain (the set of all real numbers).
Instead for the range we can see that there is a maximum at y = 4, so the range is:
R: (-∞, 4]
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Helps me please.
I’m so confused
Solve the system of equations by graphing.
x=-y
x+y=7
The graph of the system of equations shows that there is no solution to the system.
How to Solve a System of Equations by Graphing?To solve a system of equations by graphing, plot each of the lines on a graph. Then, find the point where both lines intersect each other.
The x-coordinate and the y-coordinate of the point where both lines of the equations intersect is the solution to the system.
Given the system of equations, x = -y and x + y = 7, both lines have been plotted on a graph shown below. It shows that there are is no point of intersection which means the system of equations have no solution.
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It takes Rayleigh 34 minutes complete 4 problems.
At this rate, how long will she take to complete 10
problems?
Answer:1 hour and 15 minutes
Step-by-step explanation:
so it takes her 34 minutes for 4 problems so for 2 problems its 17 minutes
and then you do the 34 times 2 because its 4 problems so you add that and that = 68 minutes and then you add 17 for the 2 problems and thats 85 minutes or 1 hour and 15 minutes
Answer:
1 hour & 25 minutes (85 minutes)
Step-by-step explanation:
Time taken for 1 problem,
→ 34 ÷ 4
→ 8.5 minutes
Now time taken for 10 problems,
→ 8.5 × 10
→ 85 minutes
Hence, answer is 85 minutes.
A washcloth is 9 inches long. If the area of the washcloth is 72 square inches, what is the width of the washcloth?
O A. 9 inches
OB. 7 inches
O C. 6 inches
O D. 8 inches
Step-by-step explanation:
Its is 8 inches as 72÷9 is 8
Find the slope of the line. 1 -4 -3 -2 1 3 -4 1 2 3 4 Simplify completely. Slope = [?] Hint: The slope of a line is the rise run
Answer:
slope = 4
Step-by-step explanation:
There are two points plotted at: ( -1 , 0) and ( 0 , 4)
slope = change in rise / change in run
slope = change in y / change in x
slope = (0 - 4) / (-1 - 0)
slope = -4/-1
slope = 4
Look at the pattern. Find the next number in the sequence using inductive reasoning 100,90,92,82,84,74,76,…
The next number in the number sequence using inductive reasoning 100,90,92,82,84,74,76,… is 66.
What is number series?
A series is a way of speaking casually of numbers. It is the total of a sequence's terms. A series of numbers is called a number series. We must identify the laws that lead to the production of a number series in order to answer the questions about number series. The questions that might arise from these topics are as varied as these series themselves.
Here the given number series,
=> 100,90,92,82,84,74,76,….
Here , first term = 100
Second term = 100-10=90
Third term= 90+2=92
Fourth term = 92-10=82
Fifth term = 82+2=84
Sixth term = 84-10=74
seventh term = 74+2=76
Eighth term= 76-10 = 66.
Therefore next term of the number Series is 66.
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In the accompanying diagram, parallel lines AB and CD are intersected by GH at E and F
respectively. If m
The measure of the angle AEG = 92°
What are corresponding angles?Corresponding angles are the angles that are formed when two parallel lines are intersected by the transversal. The opening and shutting of a lunchbox, solving a Rubik's cube, and never-ending parallel railway tracks are a few everyday examples of corresponding angles. These are formed in the matching corners or corresponding corners with the transversal.
∠CFH + ∠EFC = 180( angles on a straight line)
making ∠EFC subject and substituting ∠CFH = 2x + 20, we have
∠EFC = 180 - ( 2x + 20)
∠EFC = 180 - 2x -20
∠EFC = 160 - 2x
but ∠EFC = ∠BEF ( alternate angles are equal)
substituting their values
160 - 2x = 3x - 10
collect like terms
-2x - 3x = -10 - 160
-5x = -170
x = -170/-5
x = 34
Also ∠EFC = ∠AEG = 160 -2x ( corresponding angles are equal)
∠AEG = 160 -2X, but x = 34
∠AEG = 160 - 2(34)
∠AEG =160 - 68 = 92°
In conclusion, The value of the ∠AEG = 92°
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The
graph of a quadratic function
Find the domain and the range.
with vertex (-3, 4) is shown In the figure below.
Step-by-step explanation:
domain: x is any value, ⇒ x∈(-∝;+∝);
range: y is not greater, than 4, ⇒ y∈(-∝;4].
Dan builds identical model cars and sells them online. He records the number of models he completes every couple of hours. The graph shows Dan’s data. Choose two pairs of points on the line and calculate the slopes between them. Is Dan’s productivity constant? Explain
Yes, Dan productivity is constant and slope is given as 3/2.
What is slope?
The slope of a line is also called its gradient or rate of change. The slope formula is the vertical change in y divided by the horizontal change in x, sometimes called rise over run. The slope formula uses two points, (x1, y1) and (x2, y2), to calculate the change in y over the change in x.
Let we take one pair of point (4,6) and (2,3) and other pair of point is (6,9) and (0,0)
The slope between (4,6) and (2,3) is
m = y2-y1/x2-x1
m = 3-6/2-4
=3/2
The slope between (6,9) and (0,0)
m = 0-9/0-6
=3/2
Hence, both the slopes are equal, therefore his work is constant.
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Find the unit rate.
16 = 12
The equation has a unit rate of 3/4
How to determine the unit rate?From the question, we have the following parameters
16y = 12x
The above equation is a linear equation
In fact, it is a linear equation that shows a proportional relationship
Note that all linear equations have a constant rate of change
So, the proportional relationship is given as
16y = 12x
Make y the subject
y = 12/16x
This gives
y = 3/4x
As a general rule
A proportional relationship is represented as y = kx
Where k represents the unit rate
So, we have the following representation
y = 3/4x and y = kx
By comparing the equations
k = 3/4
Hence, the unit rate of the equation is 3/4
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Possible question
Find the unit rate.
16y = 12x
Need help finding the conclusion to this problem and the theorem that supports.
the theorems to choose from, base angles theorem, exterior angle theorem and, SAS
The thing that can be conluded about the diagram is that the ponds are the same length. This is according to the SAS theorem.
What is SAS theorem?According to the SAS theorem, if two sides and the included angle of one triangle equal two sides and the included angle of another, the triangles are congruent.
If all three corresponding sides are equal and all three corresponding angles are equal in measure, two triangles are said to be congruent. If two triangles meet one of the following criteria, they are congruent. All three corresponding side pairs are equal. Two corresponding side pairs and their corresponding angles are equal.
In this case, the triangle for the frog pond and duck pond are the same.
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There was a blizzard. Snow was falling at the rate of 3 inches per hour. If the snow keeps acclimating how long will 5 feet of snow to accumulate
The time taken for the 5 feet of snow to accumulate is 20 hours.
How to calculate the number of hours?In this case, Smsnow was falling at the rate of 3 inches per hour and if the snow keeps acclimating, we want to know how long will 5 feet of snow to accumulate.
Since 1 foot = 12 inches
5 feet = 5 × 12
= 60 inches
Therefore the time taken will be the division and this will be:
= 60 / 3
= 20
It'll take 20 hours.
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From the chart, estimate (roughly) the number of transistors per IC in 2012. Using your estimate and Moore's Law, what would you predict the number of transistors per IC to be in 2040?
The estimates for the number of transistors per IC, using Moore's Law, are given as follows:
2012: 4,194,304,000.2040: 6.87 x 10¹³.What is stated by Moore's Law?Moore's Law states that the number of transistors per IC is expected to double every two years.
From the chart shown by the image at the end of the answer, the reference number is given as follows:
4000 transistors per IC in 1972.
The number of years between 1972 and 2012 is of:
2012 - 1972 = 40.
Hence the number of doubling periods is of:
40/2 = 20 doubling periods.
Thus the estimate for the number of transistors per IC in 2012 = 20 doubling periods is of:
4000 x 2^20 = 4,194,304,000 transistors per IC.
The number of years between 1972 and 2040 is of:
2040 - 1972 = 68.
Hence the number of doubling periods is of:
68/2 = 34 doubling periods.
Thus the estimate for the number of transistors per IC in 2012 = 20 doubling periods is of:
4000 x 2^34 = 6.87 x 10¹³ transistors per IC.
Missing InformationThe chart is given by the image at the end of the answer.
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2/8+ 1/2 Least multiple that is the same: Add using renamed fractions
The addition using Least multiple, [tex]\frac{2}{8}+\frac{1}{2}[/tex] is equal to [tex]\frac{3}{4}[/tex].
What is Least Common Denominator?When two or more fractions are there, the least common denominator is the lowest number among all the common multiples of the denominators.
To find the LCD of numbers, factorization method can be used and if the numbers are co-prime then the LCD is just the multiplication of those numbers.
The denominator of given fractions is 8 and 2.
Now, finding the lowest common multiple of 8 and 2,
LCD is 8,
Now, renaming the fraction by multiplying 4 on numerator and denominator of [tex]\frac{1}{2}[/tex],
[tex]\frac{1 \times4}{2 \times4} =\frac{4}{8}[/tex]
Now, denominator is same, so adding the fractions,
[tex]\frac{2}{8}+\frac{4}{8} =\frac{2+4}{8} \\\\=\frac{6}{8}[/tex]
Dividing the numerator and denominator by 2,
[tex]\frac{6}{8} =\frac{6/2}{8/2}\\ =\frac{3}{4}[/tex]
Therefore, by adding the given fractions we get [tex]\frac{3}{4}[/tex].
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Draw out this scenario using
precise measurements and
answer the question.
You are fighting aliens and
need to shoot down a UFO. The
UFO is hovering 50 ft (10 cm) in
front and 100 ft (20 cm) in the
air above you. What angle do
you need to set your Anti
Aircraft gun to hit the UFO?
In order to hit the UFO, the Anti Aircraft gun should be set an an angle of elevation of approximately 63.435° above the horizontal in the direction of the UFO
What is an angle of elevation?An angle of elevation is an angle that the line of sight makes with the horizontal.
The location of the UFO are;
The distance of the UFO from the front of the observer (horizontal distance) = 50 feetThe distance of the UFO from above the observer (the vertical distance of the UFO) = 100 feetThe angle, θ, to which the anti aircraft gun needs to be set is found from the trigonometric ratio for tangent as follows.
[tex]tan(\theta) = \dfrac{Length \, of \, the \, side \, opposite \, to \, angle \, \theta}{Length \, of \, the \, side \, adjacent \, to \, \theta}[/tex]
The length of the side opposite to the angle θ to which the gun should be directed is the length of the height of the UFO from the observer, therefore;
Length of the side opposite to θ = 100 feet
Length of the side adjacent to θ is the length of the horizontal distance from the observer;
Length of the adjacent side to θ = 50 feet
Therefore;
[tex]tan(\theta) = \dfrac{100\, feet}{50\, feet} = 2[/tex]
tan(θ) = 2
θ is found using the inverse tangent function (arctangent) as follows;
θ = arctan(2) ≈ 63.435°
The direction the anti aircraft un should be set is at angle of elevation of approximately 63.435° above the horizontal
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A restaurant offers a game piece with each meal to win coupons for free food. The
probability of a game piece winning is 1 out of 4 and is independent of other game
pieces winning. A family orders 4 meals. Let C be the number of coupons the family
wins. What type of variable is C? Why?
The type of variable that C is can be said to be the binomial variable.
What is a binomial variable?A binomial random variable counts the number of times a specific event occurs in a given number of tries or trials. To be a binomial random variable, a variable must be There is a set number of trials.
It should be noted that the features of the binomial variable include:
1: The number of observations, n, is constant.
2: Each observation is distinct.
3: Each observation denotes one of two possible outcomes ("success" or "failure").
4: The "success" probability p is the same for each outcome.
In this case, the number of coupons the family wins illustrate a binomial.
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A sample of 144 cans of coffee showed an average weight of 16 ounces. The standard deviation of the population is known to be 1.4 ounces. Construct a 68.26% confidence interval for the mean of the population.
The 68.26% confidence interval for the mean of the population, using the z-distribution, is given as follows:
(15.88 ounces, 16.12 ounces).
What is a z-distribution confidence interval?The bounds of a z-distribution confidence interval are presented as follows:
[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]
In which the parameters are given by:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value of the z-distribution.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population. -> as the z-distribution is used when the population standard deviation is known.The confidence level is of 68.26%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.6826}{2} = 0.8413[/tex], so the critical value is z = 1.
The values of the remaining parameters are given as follows:
[tex]\overline{x} = 16, \sigma = 1.4, n = 144[/tex]
Hence the lower bound of the interval is obtained as follows:
[tex]\overline{x} - z\frac{\sigma}{\sqrt{n}} = 16 - \frac{1.4}{\sqrt{144}} = 15.88[/tex]
The upper bound of the interval is obtained as follows:
[tex]\overline{x} + z\frac{\sigma}{\sqrt{n}} = 16 + \frac{1.4}{\sqrt{144}} = 16.12[/tex]
More can be learned about the z-distribution at https://brainly.com/question/25890103
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